X-ray imaging systems may be intended for the observation of structures of very small dimensions, of the order of a few tens of nanometers wide, that may be buried at a depth of several tens of micrometers in a structure to be analyzed. Currently, X-ray tomography systems with resolutions of down to as little as 50 nanometers are available. To measure this resolution, it is therefore necessary to use resolution test charts with extremely small patterns, having widths and spacings of down to as little as a few tens of nanometers.
The resolution test charts envisaged here consist of networks of parallel (straight or curved) or radial lines of an X-ray absorbent material, such as gold, platinum, hafnium, or materials which are slightly less absorbent but easier to etch such as tungsten or tantalum or compositions based on these materials, such as tantalum nitride. The absorbent material is deposited on a substrate transparent to X-rays, for example on a thin silicon membrane, or else buried in the thickness of this substrate. For test charts of high resolution, the pattern is produced by a technique of electron beam lithography followed by plasma etching. The spacing of the lines and their width vary according to the position of the patterns in the test chart and the spacings and widths are known for each position. The resolution is read off directly by observing on the photographic or digital image of the test chart, illuminated by X-rays, the positions in which the contrast between absorbent lines is sufficient and the positions in which it becomes insufficient to properly distinguish two neighboring lines.
Given that X-rays are very penetrating, the patterns of the test chart must be sufficiently absorbent, that is to say they must not only consist of an intrinsically absorbent material but also have a sizable thickness. Moreover, the material used must be relatively easy to etch, including over a sizable height, and it is therefore not always possible to choose materials which are intrinsically the most absorbent (gold or platinum for example). For materials that are easier to etch, such as tungsten, but less absorbent, there may be a need to produce patterns whose thickness is several times larger than the width or the spacing of the patterns.
When the illumination of the test chart is carried out by a parallel X-ray beam, the measurement works well. Such is the case when the X-rays are obtained by synchrotron radiation. But in the general case, X-ray sources provide a divergent beam. If the thickness of the material is not small with respect to the width of the patterns, it results in a phenomenon of non-uniform absorption and of shadowing in respect of the X-rays which have an oblique incidence: on the one hand the absorption is not uniform throughout the width of an absorbent zone and on the other hand absorption is noted between two absorbent zones where there should not be any. The contrast thereof is greatly decreased and impairs the resolution measurement.
This is illustrated in FIG. 1 which is a transverse cut through the test chart, in a plane which contains the axis of the beam X and which is perpendicular to several parallel lines of absorbent zones. The absorbent material, of height H, is deposited on the surface of a membrane MB; it could also be buried in this membrane. The cut of an absorbent line is portrayed by a black mark. Here the lines have a constant width L and a constant spacing E which may be equal to L. The height H is greater than the width L and than the spacing E. The height or depth H of the absorbent material is measured perpendicularly to the plane surface of the membrane. The width L and the spacing E of the lines are measured perpendicularly to the parallel lines.
For X-rays incident perpendicularly to the test chart, that is to say parallel to the direction of the height of the absorbent patterns, there is no problem of shadowing (FIG. 1A); such is the case when the X-rays are provided by a non-divergent source such as a synchrotron. The spatial absorption pattern Ab which results from this non-divergent illumination is drawn alongside the pattern of absorbent zones. This absorption pattern, gathered on a photographic plate or on a digital radiological image sensor, is binary and exactly reproduces the pattern of absorbent zones; it comprises spans of constant maximum absorption where an absorbent zone is present, alternating with spans of minimum absorption, where there is none.
But for divergent X-rays provided by a conventional commercial source X (FIG. 1B), the absorption pattern Ab becomes different and all the more different the more the obliquity of the rays increases. Thus, toward the center of the test chart, the absorption pattern remains practically binary with spans of maximum absorption of width L and of spacing E. But the further one gets from the center, the more the absorption curve deforms and ceases to be binary: absorption is present over a width L′ greater than L, increasing from a minimum value up to a maximum value and returns to the minimum value, and remains at its minimum value over a width E′ of less than E. Each absorption span therefore comprises a span of maximum absorption and a progressively decreasing absorption. The contrast thereof is impaired in proportion to the obliquity of the incident rays.
The loss of contrast is all the larger the larger the height H and the larger the angle of obliquity. FIG. 1C represents this shadow effect for a larger height H than in FIG. 1B. In FIGS. 1B and 1C, the angles of obliquity are exaggerated to facilitate reading.
As the height H is dictated by the necessity to have sufficient absorption of the X-rays, there is a snag when it is desired to measure a resolution using patterns of smaller or much smaller width and spacing than this height, that is to say absorbent patterns with an aspect ratio H/L or H/E equal to 2 to 5, or indeed more.
Typically, with tungsten, there may be a need for absorbent patterns 100 nanometers in height and 25 nanometers in width. Moreover, it is not always possible to be content to have patterns of high resolution at the center of the test chart; there may be need to measure the resolution on the edges too.
This may result in the conclusion that the resolution of the imaging system is insufficient, not because it really is but because the procedure for measuring the resolution is affected by an error due to the construction of the test chart.